Metrohm Vision – Theory - Manual (Page 19)

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3.2.3 Maximum Distance
To calculate maximum distance (distance in this context is in terms of spectral value – absorbance, or
the spectral value in a derivative spectrum) of a spectrum y to a mean product spectrum x, Vision first
defines the inflated standard deviation spectrum from the product set:
s
n
x x
n i
d
j j
j
= +
−






−
−










∑
1
1
2 1 1
2
1
2
( )
( )
Where the index i runs over all wavelengths, and index j runs over all spectra in the set.
Consequently, the maximum distance is calculated as:
D abs
y x
s x
i i
i
d
overall i
=
− 













max
Maximum distance can be interpreted as the maximum deviation from the product mean spectrum
expressed in units of inflated standard deviation.
3.2.4 Correlation
Correlation formally is not a distance, but a measure of spectral similarity. Correlation between two
spectra x and y is calculated as:
D
x y
x y
c
i i
i
i
i
i
i
=
∑
∑ ∑
2 2
Strictly speaking, correlation is a dot product of two vectors representing spectra. Geometrically, it is
a cosine of an angle between those vectors. Correlation is scale invariant, i.e. its value does not
change if one or both spectra are multiplied by a constant.